While uploading files via webUI, a small box appears at the bottom-right showing the progress and it is still possible to click any links on the page. According to my experience this stops/breaks the upload. So I’d suggest to disable the rest of the page and only keep the progress box active, like a modal dialog window. Of course this will not prevent all interaction (like page reload), but may at least reduce the risk of accidential upload interruption.
An alternative solution might be to make the upload “transparent” for navigating to another library etc.? Like youtube is doing now when you go back to your last page, the video still continues in the buttom right corner.